Graphics-Related Question: Mesh and Geometry

Question

What's the difference between mesh and geometry? Aren't they the same? i.e. collection of vertices that form triangles?

Answer 1

A mesh is typically a collection of polygons/geometric objects. For instance triangles, quads or a mixture of various polygons. A mesh is simply a more complex shape.

From Wikipedia:

Geometry is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space

IMO a mesh falls under that criteria.

Answer 2

A point is geometry, but it is not a mesh. A curve is geometry, but it is not a mesh. An iso-surface is geometry, but it is not... enfin you get the point by now.

Meshes are geometry, not the other way around.

Geometry in the context of computing is far more limited that geometry as a branch of mathematics. There are only a few types of geometry typically used in computer graphics. Sprites are used when rendering points (particles), line segments are used when rendering curves and meshes are used when rendering surface-like geometry.

Answer 3

That the term "geometry" has different meanings mathematically and in rendering. In rendering it usually denotes what is static in a scene (walls, etc.) What is widely called a "mesh" is a group of geometrical objects (basically triangles) that describe or form an "object" in the scene - pretty much like envalid said it, but usually a mesh forms a single object or entity in a scene. Very often that is how rendering engines use the term: The geometrical data of each scene element (object, entity) composes that element's mesh.

Answer 4

Although this is tagged in "graphics", I think the answer connects with the interpretation from computational physics. There, we usually think of the geometry as an abstraction of the system that is to be represented/simulated, while the mesh is an approximation of the geometry - a compromise we usually have to make to be able to represent the spatial domain within the finite memory of the machine.

You can think of them basically as regular or unstructured sets of points "sprayed" on a surface or within a volume in space.

To be able to do visualization/simulation, it is also necessary to determine the neighbors of each point - for example using Delaunay triangulation which allows you to group sets of points into elements (for which you can solve algebraic versions of the equations describing your system).

In the context of surface representation in computer graphics, I think all major APIs (e.g. OpenGL) have functions which can display these primitives (which can be triangles as given by Delaunay, quads or maybe some other elements).

Answer 5

In the context implied by your question:

A mesh is a collection of polygons arranged in such a way that each polygon shares at least one vertex with another polygon in that collection. You can reach any polygon in a mesh from any other polygon in that mesh by traversing the edges and vertices that define those polygons.

Geometry refers to any object in space whose properties may be described according to the principles of the branch of mathematics known as geometry.